> ## Documentation Index > Fetch the complete documentation index at: https://nixtlaverse.nixtla.io/llms.txt > Use this file to discover all available pages before exploring further. # Daily active users Product-engagement metrics like daily active users have a recognizable shape: an underlying growth (or decay) trend, a strong weekly rhythm, and noise. `DailyActiveUsersGenerator` reproduces this for testing growth-analytics dashboards and anomaly detection on product metrics. > **The model** > > $y_t = \text{base}\,(1 + g)^{\,d(t)} \cdot w(t) + \text{boost}_t + \varepsilon_t, \qquad \text{boost decays at } (1-\delta)$ > > The level is `base_users * (1 + growth_rate)^day`, scaled on weekends > by `weekend_factor` (1.2 for gaming, 0.8 otherwise). With probability > `event_probability` per step an event adds `(impact - 1) * base` to a > boost that decays geometrically at `event_decay_rate`, where `impact` > is drawn between `event_impact_min` and `event_impact_max`. > Proportional Gaussian noise (`noise_std`) is added and the result is > clipped at zero. > > Set `growth_rate_std` to perturb the growth rate per series, and > `app_type` (`consumer`, `business`, `gaming`) to pick the defaults for > a product profile. ```python theme={null} import polars as pl import matplotlib.pyplot as plt from synforecast.generators import DailyActiveUsersGenerator ``` ## App type `app_type` sets the engagement profile, mainly through the weekend multiplier: a consumer app dips slightly at weekends, a B2B app drops sharply, and a gaming app rises. The seed and base level are shared. ```python theme={null} consumer_df = DailyActiveUsersGenerator( engine="polars", min_length=120, max_length=120, freq="D", base_users=10000.0, growth_rate=0.002, app_type="consumer", seed=42, ).generate(n_series=1) business_df = DailyActiveUsersGenerator( engine="polars", min_length=120, max_length=120, freq="D", base_users=10000.0, growth_rate=0.002, app_type="business", seed=42, ).generate(n_series=1) gaming_df = DailyActiveUsersGenerator( engine="polars", min_length=120, max_length=120, freq="D", base_users=10000.0, growth_rate=0.002, app_type="gaming", seed=42, ).generate(n_series=1) panels = [ ("consumer", consumer_df), ("business (B2B)", business_df), ("gaming", gaming_df), ] fig, axes = plt.subplots(3, 1, figsize=(12, 7.5), sharex=True) for ax, (label, df) in zip(axes, panels): ax.plot(df["ds"].to_list(), df["y"].to_list(), alpha=0.85, linewidth=1) ax.set(ylabel="Active users", title=label) axes[-1].set_xlabel("Timestamp") plt.tight_layout() plt.show() ``` ## Analyzing event impact Compare DAU on event days versus normal days to measure the lift from marketing events. ```python theme={null} event_days = consumer_df.filter(pl.col("event") == 1) if len(event_days) > 0: print("Days when events occurred:") print(event_days) avg_event_day = consumer_df.filter(pl.col("event") == 1)["y"].mean() avg_normal_day = consumer_df.filter(pl.col("event") == 0)["y"].mean() print(f"\nAverage DAU on event days: {avg_event_day:,.0f}") print(f"Average DAU on normal days: {avg_normal_day:,.0f}") print(f"Event day lift: {(avg_event_day/avg_normal_day - 1)*100:.1f}%") ``` ```text theme={null} Days when events occurred: shape: (4, 4) ┌───────────┬─────────────────────┬──────────────┬───────┐ │ unique_id ┆ ds ┆ y ┆ event │ │ --- ┆ --- ┆ --- ┆ --- │ │ cat ┆ datetime[ns] ┆ f64 ┆ i32 │ ╞═══════════╪═════════════════════╪══════════════╪═══════╡ │ 0 ┆ 2000-01-20 00:00:00 ┆ 10816.372729 ┆ 1 │ │ 0 ┆ 2000-03-22 00:00:00 ┆ 15008.853745 ┆ 1 │ │ 0 ┆ 2000-04-08 00:00:00 ┆ 21994.846532 ┆ 1 │ │ 0 ┆ 2000-04-20 00:00:00 ┆ 22292.652679 ┆ 1 │ └───────────┴─────────────────────┴──────────────┴───────┘ Average DAU on event days: 17,528 Average DAU on normal days: 12,089 Event day lift: 45.0% ``` ## Hourly active users The generator also supports sub-daily frequencies like hourly data. ```python theme={null} hourly_params = { "min_length": 168, "max_length": 168, "freq": "h", "app_type": "consumer", "base_users": 10000.0, "event_probability": 0.01, "noise_std": 0.08, "seed": 42, } hourly_gen = DailyActiveUsersGenerator(engine="polars", **hourly_params) hourly_df = hourly_gen.generate(n_series=1) print(f"Generated {len(hourly_df)} hourly observations") hourly_df.head(24) ``` ```text theme={null} Generated 168 hourly observations ``` | unique\_id | ds | y | event | | ---------- | ------------------- | ------------ | ----- | | cat | datetime\[ns] | f64 | i32 | | "0" | 2000-01-01 00:00:00 | 9275.243589 | 0 | | "0" | 2000-01-01 01:00:00 | 10272.524421 | 0 | | "0" | 2000-01-01 02:00:00 | 9468.136049 | 0 | | "0" | 2000-01-01 03:00:00 | 9727.297606 | 0 | | "0" | 2000-01-01 04:00:00 | 10144.538427 | 0 | | … | … | … | … | | "0" | 2000-01-01 19:00:00 | 13346.974807 | 1 | | "0" | 2000-01-01 20:00:00 | 12068.154452 | 0 | | "0" | 2000-01-01 21:00:00 | 10815.974473 | 0 | | "0" | 2000-01-01 22:00:00 | 11608.360831 | 0 | | "0" | 2000-01-01 23:00:00 | 10668.204221 | 0 | ```python theme={null} fig, ax = plt.subplots(figsize=(12, 4)) ax.plot(hourly_df["ds"].to_list(), hourly_df["y"].to_list(), alpha=0.8, color="C4") ax.set_xlabel("Timestamp") ax.set_ylabel("Active Users") ax.set_title("Hourly active users — consumer app (1 week)") plt.tight_layout() plt.show() ``` ## Multiple products/apps Generate DAU data for multiple products simultaneously and compare event distributions. ```python theme={null} multi_params = { "min_length": 30, "max_length": 30, "freq": "D", "app_type": "consumer", "base_users": 20000.0, "event_probability": 0.03, "seed": 42, } multi_gen = DailyActiveUsersGenerator(engine="polars", **multi_params) multi_df = multi_gen.generate(n_series=5) print(f"Generated 5 products with {len(multi_df)} total observations") print("\nProduct 0 preview:") print(multi_df.filter(pl.col("unique_id") == "0").head(10)) total_events = multi_df.group_by("unique_id").agg(pl.col("event").sum()) print("\nEvents per product:") print(total_events) ``` ```text theme={null} Generated 5 products with 150 total observations Product 0 preview: shape: (10, 4) ┌───────────┬─────────────────────┬──────────────┬───────┐ │ unique_id ┆ ds ┆ y ┆ event │ │ --- ┆ --- ┆ --- ┆ --- │ │ cat ┆ datetime[ns] ┆ f64 ┆ i32 │ ╞═══════════╪═════════════════════╪══════════════╪═══════╡ │ 0 ┆ 2000-01-01 00:00:00 ┆ 19094.054486 ┆ 0 │ │ 0 ┆ 2000-01-02 00:00:00 ┆ 20350.825855 ┆ 0 │ │ 0 ┆ 2000-01-03 00:00:00 ┆ 19354.510065 ┆ 0 │ │ 0 ┆ 2000-01-04 00:00:00 ┆ 19688.625437 ┆ 0 │ │ 0 ┆ 2000-01-05 00:00:00 ┆ 20221.064661 ┆ 0 │ │ 0 ┆ 2000-01-06 00:00:00 ┆ 15882.965767 ┆ 0 │ │ 0 ┆ 2000-01-07 00:00:00 ┆ 17069.908021 ┆ 0 │ │ 0 ┆ 2000-01-08 00:00:00 ┆ 18599.75721 ┆ 0 │ │ 0 ┆ 2000-01-09 00:00:00 ┆ 21305.138222 ┆ 0 │ │ 0 ┆ 2000-01-10 00:00:00 ┆ 22202.888052 ┆ 0 │ └───────────┴─────────────────────┴──────────────┴───────┘ Events per product: shape: (5, 2) ┌───────────┬───────┐ │ unique_id ┆ event │ │ --- ┆ --- │ │ cat ┆ i32 │ ╞═══════════╪═══════╡ │ 3 ┆ 1 │ │ 1 ┆ 1 │ │ 0 ┆ 1 │ │ 2 ┆ 1 │ │ 4 ┆ 1 │ └───────────┴───────┘ ``` ```python theme={null} fig, ax = plt.subplots(figsize=(12, 4)) for uid in multi_df["unique_id"].unique().to_list(): series = multi_df.filter(pl.col("unique_id") == uid) ax.plot(series["ds"].to_list(), series["y"].to_list(), label=uid, alpha=0.7) ax.set_xlabel("Timestamp") ax.set_ylabel("DAU") ax.set_title("Multiple products — daily active users") ax.legend() plt.tight_layout() plt.show() ``` ## Custom column names Customize the output column names to match your application’s naming conventions. ```python theme={null} custom_params = { "min_length": 30, "max_length": 30, "freq": "D", "base_users": 15000.0, "event_probability": 0.05, "event_col": "marketing_campaign", "id_col": "product_id", "time_col": "date", "target_col": "dau", "seed": 42, } custom_gen = DailyActiveUsersGenerator(engine="polars", **custom_params) custom_df = custom_gen.generate(n_series=1) print(f"Columns: {custom_df.columns}") custom_df.head(10) ``` ```text theme={null} Columns: ['product_id', 'date', 'dau', 'marketing_campaign'] ``` | product\_id | date | dau | marketing\_campaign | | ----------- | ------------------- | ------------ | ------------------- | | cat | datetime\[ns] | f64 | i32 | | "0" | 2000-01-01 00:00:00 | 14320.540864 | 0 | | "0" | 2000-01-02 00:00:00 | 15263.119391 | 0 | | "0" | 2000-01-03 00:00:00 | 14515.882549 | 0 | | "0" | 2000-01-04 00:00:00 | 14766.469078 | 0 | | "0" | 2000-01-05 00:00:00 | 15165.798496 | 0 | | "0" | 2000-01-06 00:00:00 | 11912.224325 | 0 | | "0" | 2000-01-07 00:00:00 | 12802.431016 | 0 | | "0" | 2000-01-08 00:00:00 | 18654.126716 | 1 | | "0" | 2000-01-09 00:00:00 | 18991.33087 | 0 | | "0" | 2000-01-10 00:00:00 | 18312.235462 | 0 | > **Related generators** > > * [Clickstream](clickstream) — the sessionized activity beneath > engagement metrics. > * [Seasonal](../statistical/seasonal) — the weekly rhythm in > isolation. > > Full parameters are in the [generator > reference](https://github.com/Nixtla/synforecast/blob/main/GENERATORS.md).